This presentation related to molecular diffusion of molecules in gases and liquids. Also includes inter-phase mass transfer and various theories related to it like two film theory, penetration theory and surface renewal theory.

1. Mass Transfer
Presented By:
Poonam Y. Purkar M.Pharm
E.mail : pypurkar@gmail.com
Sir. Dr. M.S.Gosavi College of Pharmaceutical Education & Research.
Nasik.

2. Contents :
 Introduction
 Molecular Diffusion
 In Gases
 In Liquid
 Mass Transfer in turbulent & laminar flow
 Interphase Mass Transfer
 Two film theory
 Penetration theory
 Surface Renewal Theory
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3. Introduction
 Transfer of material from one homogeneous phase to another
with or without phase change.
 Complex phenomenon occurs almost in all unit operations
Extraction – transfer of solute
Humidification – transfer of water molecule
Evaporation
Drying simultaneous heat & mass
Distillation transfer
 Occurs through different mechanisms such as molecular
diffusion, convection / bulk flow & turbulent mixing
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4. Mass Transfer
 Movement of the molecule occurs due to
concentration gradient known as molecular diffusion.
Molecular
Diffusion
In Gases In Liquid
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5. Molecular diffusion in gases:
partition
 Gas A moves towards chamber B and gas A towards chamber A.
 Concentration of A with distance towards chamber B & B
towards A, variation in concentration of component with
distance in the system called concentration gradient.
 Movement of molecule A or B occurs due to concentration
gradient known as molecular diffusion.
Gas A Gas B
dx
CA decreasing
CB decreasing
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6.  Fick’s law:
(negative sign, as concentration decreases with distance)
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For molecule A For molecule B
where,
DAB DBA = diffusivity of A in B & diffusivity of B in A respectively.
( cm2/sec)
NA & NB = rate of diffusion (gm.moles/ cm2/sec)
dX
dC
N
A
A 
dX
dC
DN
A
ABA 
dX
dC
DN
B
BAB 

7. Equimolecular Counter diffusion:
If molecular diffusion is the only mechanism of mass transfer then,
NA = -NB
Consider dPA and dPB are changes in partial pressure of A & B over element
dX. As we assumed that there is no bulk flow, we can say
For an ideal gas,
PAV = nA RT
where,
PA = partial vapor pressure
nA = no. of moles in volume V at temperature T.
R = gas constant
PA= CA RT ( as CA = nA/ V )
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dX
dP
dX
dP BA

RT
P
C
A
A 

8. similarly for gas B
But for equimolecular counter diffusion NA = -NB, therefore,
(as DAB = DBA =D)
where,
PA1 & PA2 are partial pressures of A at distance X1 & X2
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dX
dP
RT
D
N
BBA
B 
dX
dP
RT
D
N
AAB
A 
dX
dP
RT
D
dX
dP
RT
D
N
BBAAAB
A 

2
1
dX
dP
RT
D
N
A
A
X
X
12
AA
A
XX
PP
RT
D
N
12




9. Diffusion through stationary, non-diffusing
gas:
 Movement of molecules from liquid or film on drying solids,
occurs to a non-diffusing gas.
 Molecule A is moving from the surface to atmosphere due to
conc. gradient in partial pressure but B is not moving towards
the surface.
 Therefore, rate of mass transfer of A takes place by molecular
diffusion & bulk flow.
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10. Molecular diffusion in liquids:
According to Fick’s law, for diffusion in liquid
For equimolar counter diffusion,
where,
CA1 & CA2 = concentration of A at point x1 & x2
Diffusivity of liquid are much lesser than diffusivity of gases.
e.g.
diffusivity of gaseous ethanol in air = 0.119 cm2/sec
diffusivity of liquid ethanol in water = 1 × 10-5 cm2/sec
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12
AA
A
XX
CC
DN
12



dX
dC
DN
A
A 

11. Mass transfer in turbulent & laminar flow:
 Explained by boundary layer or film theory
 when fluid flows adjacent to the surface forms the boundary
layer
 Considers two regions
 boundary layer
 bulk
• If bulk flows in laminar fashion – rate of mass transfer
depends given by molecular diffusion equation
• If fluid bulk is turbulent – mass transfer depends upon transfer
rate across the boundary layer.
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12.  Boundary layer consist of 3 sub layers
 Laminar sub layer adjacent to surface
 Buffer / transient sub layer
 Turbulent region towards the bulk of fluid.
 Turbulent layer : eddies move under inertial forces causing
mass transfer. The rate of mass transfer is high and conc.
gradient is low
 Buffer layer : combination of eddy and molecular diffusion
responsible for mass transfer
 Laminar sub layer : molecular diffusion is the only
mechanism of mass transfer. Concentration gradient is high
and rate of mass transfer is low.
 The rate of mass transfer can be estimated by considering a
film which offers the resistance equivalent to boundary layer.
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Let,
PAi = partial pressure of A at surface
PAl = partial pressure of A at laminar sub layer
of thickness X
PAb = partial pressure of A at the edge of
boundary layer.
According to Fick’s law for diffusion,
X’ is not known , hence kg constant known as mass transfer coefficient is introduced.
We know, therefore
where, CAi & CAb concentration of A on either side of the film.
X'
P–P
entconc.gradi
bi AA

X'
P–P
.
RT
D bi AA
A N
 bi AAgA CC.k N
RT
P
C
A
A   bi AAgA CC.k N

14. Interphase Mass Transfer:
 Involves two phase mass transfer
e.g. distillation, liquid-liquid extraction.
 Different theories involved :
 Two film theory
 Penetration theory
 Surface Renewal theory
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15. Two film theory
 Theory has been developed by Nernst, Lewis and Whitman.
 Postulates that two non-turbulent fictitious films are present
on either side of the interface between thw film
 Mass transfer across these films purely occurs molecular
diffusion.
 Total resistance for mass transfer is summation of resistance
of two films
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16. 1/8/2018
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Let,
pAg = partial pressure of A in the bulk of gas
pAi = partial pressure of A in gas at the interface
CAi = concentration of A in liquid at interface
CAl = concentration of A in the bulk of liquid
kg & kl = mass transfer coefficients of individual
films of gas & liquid respectively
But difficult to know pAi and CAi.
Hence concept of overall mass transfer coefficient
is used.
pAe = gas phase partial pressure of A equilibrium
with conc. of A in the bulk of liquid (CAl)
CAe = conc. Of A in the liquid phase equillibrium
with partial pressure of A bulk gas (pAg )
KG and KL are overall mass transfer coefficient , by applying Fick’s law,
or
Equilibrium between two phases ,
pA = H CA + b
where, H & b are constant.
 eg AAGA KN pp   lAAeLA CCKN 

17.  By considering individual film transfer equations and overall
mass transfer equations, equilibrium equations can be developed
between overall and individual phase mass transfer coefficients
 If A is less soluble in liquid ( i.e. H is very large ) then
and process becomes liquid phase controlled.
 If A is highly soluble in liquid ( i.e. H is very low ) then KG ≈
kg and process is gas phase controlled.
 According to this theory, mass transfer is directly proportional
to molecular diffusivity of solute in the phase into which it is
going and inversely proportional to thickness of films
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lk
H
k
1
K
1
gG

lk
1
Hk
1
HK
1
K
1
gGL

H
k
KG
l


18. Penetration theory:
 This theory proposed by Higbie
 considers unsteady state at interface
 Fluid eddies travel from bulk to interface by convection &
remain remain there for equal but limited period of time
 When eddies comes at interface, solute moves into it by
molecular diffusion & get penetrated into bulk when eddies
moves to bulk.
 According to this theory, rate of mass transfer directly
proportional to square root of molecular diffusion and
inversely proportional to exopsure time of eddies at interface.
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MSGCOPER, Nasik

19. Surface renewal theory:
 This theory proposed by Dankwort
 Each eddies gets equal exposure time at interface
 Continuous renewal of interface by fresh eddies which have
composition that of bulk
 Turbulent eddies remain at interface for time varying from 0
to ∞ and taken back into bulk phase by convection current.
 According to this theory, rate of mass transfer is directly
proportional to square root of molecular diffusivity.
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20. Thank you
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